Parametric model order reduction (pMOR) aims to reduce the marginal (i.e., in the limit of many queries) cost associated with the solution to a parametric system over a range of parameters. pMOR techniques rely on the construction of a low-rank approximation of the solution field: the inadequacy of linear approximations to deal with parametric fields with sharp gradients fundamentally hinders the application of linear-subspace model reduction to advection-dominated problems. For this reason, several authors have proposed nonlinear approximation techniques to overcome limitations of linear methods. This work is focused on the development of a registration-based model reduction procedure, which relies on the introduction of a geometric parameterised mapping to track parameter-dependent flow features and ultimately improve performance of linear compression methods. This approach can provide efficient ROMs which require a relatively small training database even in the presence of non-linear phenomena and can be exploited to speed-up the optimization of industrial components. The proposed approach is assessed on two test cases:the flow in a turbofan air intake and the flow around the LS89 cascade. A database of high-fidelity solutions for several working conditions is obtained by means of Reynolds-averaged Navier-Stokes (RANS) simulations. The registration method allows to perform non-linear interpolations to predict out-of-samples solutions. Prediction error and choice of tracking flow features are discussed.